Tarte--Math--Pascal's Triangle--challenge-prize

[skilespaul]

I will admit that I never did well in math, in school. At about the age of 10, I started needing glasses to see, but I never got glasses until I was about 13. By that time I was far behind the other kids in math, because I couldn't see what was written on the chalkboard well enough. Because I was so far behind, some math teachers treated me like I was stupid. therefore I developed a dislike for math, which lasted years. However, I found this video very interesting. Ed does a great job teaching.

[11889music]

Wait..... How do I pause? 

[MaxReason]

It's implied but the constraint should be explicitly stated, that the paths to a given box may never be up; that you can only traverse down to the left or down to the right, never up-left nor up-right. Otherwise the number of paths is infinite.

Another way to express this is that given a row, the next step must be to a row below the current row.

[edwardtarte]

@MaxReason, I said it, explicitly, at 1:27: "following those paths, downward, from the top". So a person who listens to me carefully will probably not be inclined to make a comment such as yours.

[BIJMOZ]

I'm way past my math class days but this was really interesting :)

[Kargoneth]

Woah... I was looking up Pascal's triangle on Wikipedia and they mention Pascal's pyramid and Pascal's simplex. The latter two of which are much harder to draw on a two-dimensional surface but can still be visualized.

Darn it, Ed. You make me intrigued by such things!

Pascal's triangle even contains my favourite number sequence: (0), 1, 3, 6, 10, 15, ...

Sadly, as your video points out, it doesn't contain the sequence for my favourite curve, the parabola. I will *make* it contain it!

[Kargoneth]

An audiophile of my selection? Can you email yourself to me, Ed? You're and audiophile, aren't you? :)

(Oh ho ho! So punny!)

[Kargoneth]

@Kargoneth

*You're an audiophile

[TheINTPMagician]

I see the pattern in the triangle... just not why... after a few days (so people have a chance to figure it out) can you explain it to us?

[edwardtarte]

@TheINTPMagician, go to my profile page and message me where you see the pattern. Then if you want a hint about why, I can probably give you one. For now, I don't want to explain it to all, because I want this puzzle to remain available.

[blabby102]

Very interesting videos. Thank you!

[blackplatypus]

Recreational mathematics is awesome.

btw, has anyone ever noticed that if height = A and radius = Z

Then the mathematical volume of a Pizza is PiZZA?

[edwardtarte]

@blackplatypus, very clever. That reminds me: write 3.14 on a piece of paper so that when you perhaps hold it up to the light you can see it from the back.  Write the 4 as it appears here in print, with the top closed instead of open. Then look at the 3.14 from the back. What do you see?

[ThoroughbredofSin]

@edwardtarte That's Great!

[green10goo]

@edwardtarte I don't understand, could you explain a little more? where do you write the second 4? and at then end, when you say "back" do you mean the same back where you wrote 4 again, or turn it around to the 3.14?

[DeluxeWarPlaya]

@edwardtarte It's easier to explain that same principle by asking to write 3.14 and reading it in a mirror

[Checker222]

Wow, I am in awe - Awesome brain twister sir!

[thalamay]

I got the hidden squares...still no idea about a geometrical interpretation...I'm working on it ;)

[sheri226]

It hurts my brain to even try to figure this out. Math is one of the reasons I became a nurse, we don't have to have it : )

[fractal420]

@sheri226 Give him 20 ccs of this stuff! or was it 200? Doh! :)

[sheri226]

@fractal420 What we administer is already in vials.. not much math in nursing at all, you would probably be surprised. The only math we need to graduate is Algebra 1 and that was pretty easy. It's the pills that usually require the math. IV drips used to be counted and required math but all that ended when the IV poles became electronic and the bags became prefilled, hell even the syringes come prefilled now. I admit I would need a calculator if I ever worked in out in a field.

[shogo7g]

Will we ever get an explanation as to how your puzzles can be solved?

[edwardtarte]

@shogo7g, for the time being, I sometimes give hints to individuals and sometimes complete solutions to individuals.

[Steidemeister56]

blaise pascal isn´t that this religous loon?

[manhattanwombat]

@Steidemeister56 thats jean calvin

[fractal420]

@Steidemeister56 Newton believed in a god and dabbled in alchemy but that doesn't take away from his achievements. :)

[Rocky183]

Are you gonna make a video answering these challenges? I can't solve them myself, but I find them very interesting.

[TheUnillogical]

binomial expansion

[beechgrovejoe]

How about a video about the mathmatical definitions of the terms "hypothesis", "theory", and "law".

[edwardtarte]

@beechgrovejoe, thank you for the suggestion. My initial reaction is that such a video would be rather dry, academic, and perhaps dull; and probably I could not do a very good job of it anyway.

[Steidemeister56]

@edwardtarte oh don´t be so shy, i´m sure you´d do a great job

[beechgrovejoe]

@edwardtarte I agree it could be dry and academic. But it would make a great contrast to the definitions used by both average people and scientists. Math's definition is very precise. The ones used by normal people and science is no where near as clear as the definitions from mathamatics.

[LordCustos3]

@edwardtarte

User Atheistblindchick made a very good video on (almost) that subject. (watch?v=BPA3E5PD3Kc)

I guess I'd sum it the differences between "Hypothesis", "Theory" and "Law" like this:

Hypothesis == Educated Guess, written down to be verified/falsified by experiment.

Theory == Proven True by documented, repeated independent experiments.

Law == An equation that is true under nearly every known circumstance.

[Prophiscient]

@beechgrovejoe

In the context of evolution, these terms are all explained on "not just a theory dotcom". (Close the spaces and use your imagination to turn this into a URL.)

[beechgrovejoe]

@Prophiscient I specifically don't want any definition from some science fanboy site. Their definitions are always biased toward the science definition. I am looking for someone to make a video from a math perspective. In math the definitions are VERY precise and don't require experiments that can be interpeted differently or consider things that work nearly all the time.

[QuarkyGideon]

Is Blaise Pascal the founder of Pascal's wager also?

I must also ask will we ever recieve solutions to these challenges?

[edwardtarte]

@QuarkyGideon, yes, so we now have a connection between my math videos and my 'religious' videos:)

[QuarkyGideon]

@edwardtarte

I suppose his wager never got far in mathematics? hahaha...

[Prophiscient]

@QuarkyGideon

He is also the man the the programming language Pascal was named after, and his name is a unit for (air) pressure. 1 Pa = 1 N/m². (Outdated: 1 hPa = 1 millibar.)

[sp4zzer]

The pattern is quite easy to catch, but figuring out how to explain it geometrically..w ell lets say my boss would kill me for that priority of time ;) I'll try to be back later

[GMNives]

I love these videos. Thank you so much for proposing these interesting and novel little bits of information.

[Martyj2009]

If I remember right this is used in multiplying (a + b) ^n where N is the row.

[edwardtarte]

@Martyj2009, that is true, and a very good challenge is to figure out and explain why those numbers of P's Triangle actually are the correct coefficients in a binomial expansion:) As with so many math things, my fellow math teachers at the high school where I taught never taught the reason behind it. And that is too bad.

[zarkoff45]

Your prize might would be more interesting to me if you would play a composition I wrote. Would you take a midi file by email and try to play it?

[edwardtarte]

@zarkoff45, I will try, but I make no promises, since I am not very good at that sort of thing. Go ahead.